Hello, Grade 3 students! Let's get to know some bigger numbers!
In this lesson, we will go beyond the thousands and get to know numbers up to 100,000! Did you know that we see these numbers in real life all the time? For example, the price of a motorcycle, the amount of savings in a bank account, or the total number of students in a province.
If these big numbers make your head spin, don't worry! We will learn them together, step by step. You'll definitely understand them in no time!
1. Reading and Writing Numbers
We can write numbers in three ways: Hindu-Arabic numerals, Thai numerals, and words.
Important Tip: Don't forget to add a comma (,) every three digits, counting from the right, to make the numbers easier to read!
Example:
Hindu-Arabic: 45,678
Thai numerals: ๔๕,๖๗๘
Words: forty-five thousand six hundred seventy-eight
Fun Fact!
Whenever a number has 2 or more digits and ends in 1 in the ones place (like 11, 21, 101), we always pronounce that "1" as "et" in Thai. For example, 21,501 is read as twenty-one thousand five hundred "et".
Common Mistakes: Many students often forget to write the words "ten thousand" or "thousand", or they mix them up. Always check the place value carefully before you write it down!
2. Place Value and Digit Value
Every digit has its own "home," which we call its place, and each place has a different "power" or value.
Let's look from right to left (from smallest to largest):
• Ones place: Has the value of the digit itself (e.g., 5 has a value of 5)
• Tens place: Has a value in tens (e.g., 5 in this place has a value of 50)
• Hundreds place: Has a value in hundreds (e.g., 5 in this place has a value of 500)
• Thousands place: Has a value in thousands (e.g., 5 in this place has a value of 5,000)
• Ten-thousands place: Has a value in ten-thousands (e.g., 5 in this place has a value of 50,000)
Example: The number 72,034
7 is in the ten-thousands place, has a value of \( 70,000 \)
2 is in the thousands place, has a value of \( 2,000 \)
0 is in the hundreds place, has a value of \( 0 \)
3 is in the tens place, has a value of \( 30 \)
4 is in the ones place, has a value of \( 4 \)
Important Tip: The digit 0 always has a value of 0, no matter where it is. However, we can't do without it because it acts as a "placeholder" to keep other digits in their correct positions.
3. Expanded Form
Writing in expanded form means adding up the value of the digits in each place.
Simple Secret Formula: Break down the number according to its value and connect them with plus (+) signs.
Example: 84,512 can be written in expanded form as:
\( 84,512 = 80,000 + 4,000 + 500 + 10 + 2 \)
Quick Summary: Expanding a number is like taking a toy apart to see how much each individual piece is worth!
4. Comparing Numbers
When you have two numbers, how do you know which one is bigger? Just follow these steps:
Step 1: Count the number of digits first.
The number with more digits is always greater! For example, 10,000 (5 digits) is definitely greater than 9,999 (4 digits).
Step 2: If the number of digits is the same, look from the "far left."
Start at the ten-thousands place; whoever has the larger digit wins! If they are the same, move to the next digit to the right (thousands, hundreds...) until you find digits that are different.
Symbols to remember:
> means greater than (the wide mouth always points toward the larger number)
< means less than
= means equal to
5. Ordering Numbers
Once you know how to compare, ordering numbers is a piece of cake! There are two ways:
1. Ascending order: Find the smallest number first and work your way up.
2. Descending order: Find the largest number first and work your way down.
Recommended Technique: If you have a group of numbers, find the largest and smallest ones and place them at the ends first. Then, fill in the rest in the middle. This will help you stay organized!
6. Number Patterns
A pattern is a series of numbers related in a "systematic" way. You need to be a detective to figure out how the set of numbers is changing.
• Increasing patterns: E.g., increasing by 3, by 5, or by 100 (using addition)
Example: 100, 200, 300, 400... (increasing by 100)
• Decreasing patterns: E.g., decreasing by 2, by 50, or by 1,000 (using subtraction)
Example: 5,000, 4,000, 3,000, 2,000... (decreasing by 1,000)
How to find the answer: Try subtracting two adjacent numbers to see exactly how much it increases or decreases each time!
Final Wrap-up: Math isn't scary! As long as you understand the "place value" system, numbers in the tens of thousands become easy. Just keep practicing reading, writing, and observing how the values work. You can do it, smarty-pants!